Need advice, please

A Co-Worker of mine has been having issues with her cat since she was a kitten. She has went to many vets and they say nothing is wrong with her.

She was feeding her cat Iams dry and the cat would throw up almost every other day after eating. I told her she should switch to a better food and she started using the Blue Buffalo. It was working really good for her, only throwing up once a week but her skin started to get all scabby and dry. She took the cat back to the vet and they put her on HILLS Z/D. This has helped with her skin problem but she is now vomiting again.
Does anyone have any opinions on what she should do next? I told her she should try the Natural Balance Green Pea and Duck but said I wanted some other opinions.
Thanks!

Is she willing to feed canned rather then dry. Problem with dry is you can't really just "change" brands - they have more problems adjusting to a quick change over.

Talk with the vet... I think royal canin makes a skin and coat RX maybe try that or yes a limited ingredient diet ( I personally would try a NON poultry )

Thank you for the help.
She is bringing the cat back in on Saturday for more blood work. I hope they figure out what is causing the problem.